How their supporters now hope that similar strides forward can be made in the manner the Ibrox club conducts its business at boardroom level.
At no stage last season did Ally McCoist's team manage to kill off the challenge of their opponents away from home as convincingly as they did on Saturday.
They romped into a 3-0 lead at half-time courtesy of an opportunistic strike by Andy Little and well-taken goals from Lewis Macleod and Lee McCulloch.
Whatever dreams the home fans who had crammed into a sun drenched Stair Park harboured of their team pulling off an upset were rapidly killed off.
The style of football the visitors played at times as they picked up another three League One points was also hugely encouraging for their manager.
Nicky Law, operating in his favoured central midfield berth in a 4-4-2 formation, continued his impressive start to life as a Rangers player.
His presence in the starting line-up once again brought out the best in Ian Black who was unfortunate not to open the scoring early on.
Little, Macleod and Dean Shiels are also clearly flourishing thanks to the presence of fresh faces in a side that had become decidedly stale.
The fact no fewer than nine players have netted for Rangers so far in the 2013/14 campaign underlines how much this side has improved.
Little and McCulloch were responsible for the vast majority of goals the Glasgow club scored last term. The pair bagged over 50 between them in the Third Division.
That players in every department - in defence, in midfield and in attack - are getting their names on the scoresheet proves this is a far more complete unit than before.
McCoist agreed: "We have asked the midfielders to chip in with more and they have responded.
"I have always been a big fan of strikers scoring. But it is very pleasing to get goals from other areas."
Despite keeping a clean sheet, Rangers were not at their best defensively in Stranraer. Indeed, they needed the excellent Scott Gallagher to save them on several occasions.
Gallagher had to be sharp, for instance, when Frank McKeown was allowed a free header at goal early in the second half after his team was awarded a free-kick in a dangerous area.
Still, Emilson Cribari and Chris Hegarty, who had both played at centre-half in the 4-1 triumph over Brechin City the week before, were ruled out injured.
It spoke volumes for the positive outlook that currently exists at Rangers that McCoist was upset his side failed to build on their lead in the second half in Wigtownshire.
"I was disappointed that we failed to show more of a killer instinct in the second half against Stranraer when we were 3-0 ahead," he said.
"If I had been playing in that game I would have seen it as a perfect opportunity to batter a few more goals in and get my tally up.
"We have to be more clinical in our approach, try to score more goals and kill teams off. We have to try and play with the same commitment for 90 minutes."
THE Rangers manager added: "There are reasons for it. But I felt the need to point out to the players after the game.
"We have to play for the duration of the match and not just in patches."
Once again, the Light Blues faithful who had travelled down the A77 in their numbers were left to speculate on how well the team will perform after August 31.
That is the final day of the SFA signing embargo. The Third Division champions will then be able to play all eight of their new recruits from September 1.
They have done rather well so far with just two trialists - Jon Daly and Law got the nod to play once again in Wigtownshire - present in their ranks.
With the likes of Bilel Mohsni, Arnold Peralta, Richard Forster, Nicky Clark and Stevie Smith all becoming available to play in the same starting XI next month, Rangers should improve further still.
With the diabolical away form that dogged the Ibrox club last season now a distant memory their followers should have every reason to be happy with their outlook on the park.
Of course, the continuing instability at the Glasgow institution, as rival groups of shareholders jostle for control, is a source of very real concern for every one of them.
A hastily-arranged board meeting will be held tomorrow evening to discuss the position of controversial former chief executive Charles Green at Rangers.
The now paid consultant has angered many, including manager McCoist, with his public comments since making a surprise return to the club.
In addition, rumours that another financial crisis is looming at a club that banked £22million last year following a share offering persist.
With the future appearing far brighter on the football front, clarity, transparency and unity elsewhere would be greatly welcomed by everyone concerned with Rangers.